It was their fourth victory in 21 Tests in England over 40 years and their first since a 1-0 victory in a two-Test series 10 years ago
Chasing 160 to win, Deccan Chargers were cruising well towards victory before a middle order upset saw them bowled out for 157 in 19.5 overs.
Rohit Sharma was the only player to provide some resistance scoring 73.
Earlier Shane Watson cracked a scintillating 36-ball 58 but Rajasthan Royals suffered a middle-order batting collapse to be dismissed for 159
Watson blasted three fours and as many sixes to stand amidst the ruins, even as Michael Lumb (15), Naman Ojha (1), Yusuf pathan (5), Abhishek Jhunjhunwala (11) and Abhishek Raut (0) were dismissed cheaply. Watson played a dashing knock to anchor the Rajasthan innings but their batting capitulated as they lost first half of their side for 130 in 15.2 overs
It was their fourth victory in 21 Tests in England over 40 years and their first since a 1-0 victory in a two-Test series 10 years ago
The visitors seem set to claim victory on Monday, barring yet another twist in a Test match full of them
Virat Kohli also returns to the Test team after he missed the five matches against England at home due to the birth of his second child
The first Asian-origin cricketer to captain England in T20Is, Ali has scored five centuries in tests and three in ODIs, also taking 366 wickets across all three formats
The former all-rounder has returned to cricket during the past year after a horrific car crash at the end of 2022
Three stadiums in Pakistan are undergoing renovation work for next year's Champions Trophy
The T20 series will be played between September 11-15 with the ODI series taking place from September 19-29
ICC Chief Executive Geoff Allardice along with other ECB officials was also present on the occasion